Convergence of ADMM for convex programs is well established [1]}, [2]}, [3]}, [4]}. However, convergence typically holds under some technical conditions, which have to be verified for the optimization problem at hand. Unlike standard optimization problems where the variable is a vector, the optimization variable in (REF ) is a matrix. However, both vectors and matrices can be seen as elements of some finite-dimensional inner-product space and existing convergence results can be extended in a straightforward manner to this more general setting [3]}. In particular, as explained next, the ADMM convergence results in [4]} can be applied to our problem.
